Find the $$ y $$-coordinate of the $$ y $$-intercept of the polynomial function defined below. $$ f(x)=-2(2 x-6)(x-6) $$

Question

UpStudy AI · Accepted Answer

To find the $$ y $$-coordinate of the $$ y $$-intercept for the polynomial function $$ f(x) = -2(2x - 6)(x - 6) $$, follow these steps:

1. **Identify the $$ y $$-intercept:**
   The $$ y $$-intercept occurs where $$ x = 0 $$.

2. **Substitute $$ x = 0 $$ into the function:**
   $$
   f(0) = -2(2(0) - 6)(0 - 6)
   $$
   $$
   f(0) = -2(-6)(-6)
   $$

3. **Calculate the value:**
   $$
   f(0) = -2 \times 36 = -72
   $$

Therefore, the $$ y $$-coordinate of the $$ y $$-intercept is $$-72$$.

$$\boxed{-72}$$
The $$ y $$-coordinate of the $$ y $$-intercept is $$-72$$.

Find the \( y \)-coordinate of the \( y \)-intercept of the polynomial function defined below. \[ f(x)=-2(2 x-6)(x-6) \]